TY - JOUR
T1 - Local rigidity of Lyapunov spectrum for toral automorphisms
AU - Gogolev, Andrey
AU - Kalinin, Boris
AU - Sadovskaya, Victoria
N1 - Publisher Copyright:
© 2020, The Hebrew University of Jerusalem.
PY - 2020/7/1
Y1 - 2020/7/1
N2 - We study the regularity of the conjugacy between an Anosov automorphism L of a torus and its small perturbation. We assume that L has no more than two eigenvalues of the same modulus and that L4 is irreducible over ℚ. We consider a volume-preserving C1-small perturbation f of L. We show that if Lyapunov exponents of f with respect to the volume are the same as Lyapunov exponents of L, then f is C1+Hölder conjugate to L. Further, we establish a similar result for irreducible partially hyperbolic automorphisms with two-dimensional center bundle.
AB - We study the regularity of the conjugacy between an Anosov automorphism L of a torus and its small perturbation. We assume that L has no more than two eigenvalues of the same modulus and that L4 is irreducible over ℚ. We consider a volume-preserving C1-small perturbation f of L. We show that if Lyapunov exponents of f with respect to the volume are the same as Lyapunov exponents of L, then f is C1+Hölder conjugate to L. Further, we establish a similar result for irreducible partially hyperbolic automorphisms with two-dimensional center bundle.
UR - https://www.scopus.com/pages/publications/85086108591
UR - https://www.scopus.com/pages/publications/85086108591#tab=citedBy
U2 - 10.1007/s11856-020-2028-6
DO - 10.1007/s11856-020-2028-6
M3 - Article
AN - SCOPUS:85086108591
SN - 0021-2172
VL - 238
SP - 389
EP - 403
JO - Israel Journal of Mathematics
JF - Israel Journal of Mathematics
IS - 1
ER -